Consider the functon

Question

Consider the function f(x)=(2/x^2)-(7/x^6). Let F(x) be the antiderivative of f(x) with F(1)=0.

Then F(x)=_____?

Answer 1

f(x) = 2/x² - 7/x⁶

 

F(x) = -2/x + (7/5)/x⁵ + c

 

F(1) = 0 = -2 + 7/5 + c = -10/5 + 7/5 + c = -3/5 + c

 

c = 3/5

 

F(x) = -2/x + (7/5)/x⁵ + 3/5

 

(By the way, thank you for using parentheses!)